# Chapter title

```Cost-Volume-Profit
Relationships
EMBA 5403 Fall 2010
Cost Estimation 1
Constant
Std Err of Y Est
R squared
No. of Observations
Degrees of Freedom
X Coefficient(s)
Std Err of Coef.
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250
299.304749934466
0.944300518134715
5
3
6.75
0.9464847243
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Estimation (continued)
The results gives rise to the following equation:
Utility Costs = &pound;250 + (&pound;6.75 x # of units produced)
R2 = .944, or 94.4 percent of the variation in setup costs is
explained by the number of setup hours variable.
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Estimation (continued)
Given:
*T-value for sample size of 5 at 95% confidence level is 3.182 (two-tale
test and 3 degrees of freedom)
*Standard error of estimate for this sample at the 95% confidence level
is 598.6
The confidence interval for 300 units is:
TC = &pound;250 + 6.75 (300) + (3.182 x &pound;598.6)
= &pound;2275 + &pound;1911
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Cost Estimation Example 2
 In each month, Exclusive Billiards produces between 4 to
10 pool tables. The plant operates on 40-hr shift to
produce up to seven tables. Producing more than seven
tables requires the craftsmen to work overtime. Overtime
work is paid at a higher hourly wage. The plant can add
overtime hours and produce up to 10 tables per month.
The following table contains the total cost of producing
between 4 and 10 pool tables.
Required: a. compute average cost per pool table for 4 to 10 tables
 Estimate fixed costs per month.
Pool Tables Total Cost
4
62800
5
66000
6
69200
7
72400
8
75800
9
79200
10
82600
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Cost-Volume-Profit Analysis

Examines the behavior of total revenues, total costs, and
operating income as changes occur in the output level, selling
price, variable costs or fixed costs

helpful to understand the relationship among variable costs, fixed costs
and profit
Assumptions of CVP Analysis
1. revenues change in relation to production and sales
2. costs can be divided in variable and fixed categories and fixed
element constant over the relevant range
3. revenues and costs behave in a linear fashion
4. costs and prices are known
5. if more than one product exists, the sales mix is constant
6.
inventories stay at the same level
7. we can ignore the time value of money
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Page 67
Contribution Margin
 Contribution margin is equal to the difference between
total revenue and total variable costs
Contribution margin per unit
= Selling price - Variable cost per unit
Contribution margin percentage
= Contribution margin per unit / selling price per unit
Per Unit
Revenue
Variable costs
Contribution margin
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\$200
120
\$80
Total for
2 units
\$400
240
\$160
%
100%
60%
40%
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Pages 68 - 69
Contribution Margin Income
Statement
 Income statement that groups line items by cost
behaviour to highlight the contribution margin
0
Revenue
Packages Sold
1
2
25
40
\$0
\$200
\$400\$5,000 \$8,000
Variable costs
0
120
240 3,000 4,800
Contribution margin
0
80
160 2,000 3,200
2,000
2,000
2,000 2,000 2,000
Fixed costs
Operating income\$(2,000)\$(1,920)\$(1,840) \$0 \$1,200
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Page 69
Breakeven Point
 Quantity of output where total revenues equal total
costs
 Point where operating income equals zero
Breakeven point in units
= Fixed costs / Contribution margin per unit
= \$2,000 / \$80
= 25 units
Breakeven point in dollars
= Fixed costs / contribution margin %
= \$2,000 / 40%
= \$5,000
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Page 71
Cost-Volume-Profit Graph
\$10,000
Total revenues
line
Breakeven
Point
25 units
\$8,000
Total costs
line
\$6,000
Operating
income
\$4,000
\$2,000
Operating
loss
\$0
0
10
20
30
40
50
Units Sold
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Page 72
Target Operating Income
 For most firms in the private sector, the main
objective is not to breakeven
 Convert after-tax desired net income to its
before-tax equivalent operating income
Target operating income
= Target net income / (1 - tax rate)
Target Unit Sales
= (Fixed costs + Target operating income)
/ Contribution margin per unit
Target Dollar Sales
= (Fixed costs + Target operating income)
/ Contribution margin %
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Pages 73 - 75
Sensitivity Analysis
 sensitivity analysis is a “what-if” technique that
examines how a result will change if the original
predicted data are not achieved or if an underlying
assumption changes
 What will happen to operating income if volume
declines by 5%?
 What will happen to operating income if variable
costs increase by 10% per unit?
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Pages 76 - 77
Alternative Cost Structures
 CVP helps managers assess the risks and potential
benefits of adopting alternative cost structures
Example: Alternative rental arrangements
Option 2
\$1,400 Fixed Fee
+ 5% Commission
Option 1
\$2,000 Fixed Fee
Rev
\$
Rev
\$
Cost
Units
Breakeven = 25 units
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Option 3
20% Commission
Rev
\$
Cost
Cost
Units
Units
Breakeven = 20 units
Breakeven = 0 units
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Pages 77 - 78
Basics of Cost-Volume-Profit
Analysis
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CM is used first to cover fixed
expenses. Any remaining CM
contributes to net operating income.
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The Contribution Approach
Sales, variable expenses, and contribution margin can
also be expressed on a per unit basis. If Racing sells
generated to cover fixed expenses and profit.
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The Contribution Approach
Each month Racing must generate at least
\$80,000 in total CM to break even.
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The Contribution Approach
If Racing sells 400 units in a month, it will be
operating at the break-even point.
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The Contribution Approach
If Racing sells one more bike (401
bikes), net
operating income will increase by \$200.
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The Contribution Approach
We do not need to prepare an income statement
to estimate profits at a particular sales volume.
Simply multiply the number of units sold above
break-even by the contribution margin per unit.
If Racing sells
430 bikes, its
net income will
be \$6,000.
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CVP Relationships in Graphic Form
The relationship among revenue, cost, profit and
volume can be expressed graphically by
preparing a CVP graph. Racing developed
contribution margin income statements at 300,
400, and 500 units sold. We will use this
information to prepare the CVP graph.
Income
300 units
Sales
\$ 150,000
Less: variable expenses
90,000
Contribution margin
\$
60,000
Less: fixed expenses
80,000
Net operating income
\$ (20,000)
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Income
400 units
\$ 200,000
120,000
\$ 80,000
80,000
\$
-
Income
500 units
\$ 250,000
150,000
\$ 100,000
80,000
\$ 20,000
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CVP Graph
450.000
400.000
350.000
300.000
250.000
In a CVP graph, unit volume is
usually represented on the
horizontal (X) axis and dollars on
the vertical (Y) axis.
200.000
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
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CVP Graph
450.000
400.000
350.000
300.000
250.000
200.000
Fixed Expenses
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
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CVP Graph
450.000
400.000
350.000
300.000
250.000
Total Expenses
200.000
Fixed Expenses
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
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CVP Graph
450.000
400.000
Total Sales
350.000
300.000
250.000
Total Expenses
200.000
Fixed Expenses
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
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CVP Graph
450.000
Break-even point
(400 units or \$200,000 in sales)
400.000
350.000
300.000
250.000
200.000
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
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Contribution Margin Ratio
The contribution margin ratio is:
CM Ratio =
Total CM
Total sales
For Racing Bicycle Company the ratio is:
\$80,000
= 40%
\$200,000
Each \$1.00 increase in sales results in a
total contribution margin increase of 40&cent;.
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Contribution Margin Ratio
Or, in terms of units, the contribution margin
ratio is:
CM Ratio =
Unit CM
Unit selling price
For Racing Bicycle Company the ratio is:
\$200 = 40%
\$500
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Contribution Margin Ratio
400 Bikes
Sales
\$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
\$
-
500 Bikes
\$ 250,000
150,000
100,000
80,000
\$ 20,000
A \$50,000 increase in sales revenue
results in a \$20,000 increase in CM.
(\$50,000 &times; 40% = \$20,000)
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CONTRIBUTION MARGIN RATIO
CMR= CONTRIBUTION MARGIN RATIO
= CM / SALES OR cmu/p
VCR = VARIABLE COST RATIO
= VC/SALES OR vcu/p
CMR +VCR= 1
EFFECT OF CHANGE IN FIXED COSTS?
EFFECT OF CHANGE IN VARIABLE COSTS?
EFFECT OF CHANGE IN SELLING PRICE?
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Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average selling
price of a cup of coffee is \$1.49 and the average
variable expense per cup is \$0.36. The average
fixed expense per month is \$1,300. 2,100 cups
are sold each month on average. What is the CM
Ratio for Coffee Klatch?
a. 1.319
b. 0.758
c. 0.242
d. 4.139
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Quick Check 
Coffee Klatch is an espresso stand in a downtown
office building. The average selling price of a cup of
coffee is \$1.49 and the average variable expense per
cup is \$0.36. The average fixed expense per month
is \$1,300. 2,100 cups are sold each month on
average. What is the CM Ratio for Coffee Klatch?
a. 1.319
b. 0.758
Unit contribution margin
CM Ratio =
Unit selling price
c. 0.242
d. 4.139
(\$1.49-\$0.36)
=
=
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\$1.49
\$1.13
= 0.758
\$1.49
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Changes in Fixed Costs and Sales
Volume
What is the profit impact if Racing
can increase unit sales from 500
to 540 by increasing the monthly
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Changes in Fixed Costs and Sales
\$80,000 + \$10,000 advertising = \$90,000
Volume
Sales increased by \$20,000, but net operating
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income
decreased
by
\$2,000.
EMBA 5403
Changes in Fixed Costs and Sales
Volume
The Shortcut Solution
Increase in CM (40 units X \$200)
Decrease in net operating income
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\$ 8,000
10,000
\$ (2,000)
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Change in Variable Costs and Sales
Volume
What is the profit impact if Racing can
use higher quality raw materials, thus
increasing variable costs per unit by \$10,
to generate an increase in unit sales
from 500 to 580?
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Change in Variable Costs and Sales
Volume
580 units &times; \$310 variable cost/unit = \$179,800
Sales increase by \$40,000, and net operating income
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increases
by
\$10,200.
EMBA 5403
Change in Fixed Cost, Sales Price and Volume
What is the profit impact if Racing (1) cuts its selling
price \$20 per unit, (2) increases its advertising budget
by \$15,000 per month, and (3) increases unit sales
from 500 to 650 units per month?
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Change in Fixed Cost, Sales Price and
Volume
Sales increase by \$62,000, fixed costs increase by
\$15,000,
and net operating income increases by \$2,000.
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EMBA 5403
Change in Variable Cost, Fixed Cost and Sales Volume
What is the profit impact if Racing (1) pays a \$15 sales
commission per bike sold instead of paying salespersons flat
salaries that currently total \$6,000 per month, and (2) increases
unit sales from 500 to 575 bikes?
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Change in Variable Cost, Fixed Cost and Sales Volume
Sales increase by \$37,500, variable costs increase by
\$31,125, but fixed expenses decrease by \$6,000.40/109
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Change in Regular Sales Price
If Racing has an opportunity to sell 150 bikes to a
wholesaler without disturbing sales to other customers
or fixed expenses, what price would it quote to the
wholesaler if it wants to increase monthly profits by
\$3,000?
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Change in Regular Sales
Price
\$ 3,000 &divide; 150 bikes =
Variable cost per bike =
Selling price required =
\$ 20 per bike
300 per bike
\$ 320 per bike
150 bikes &times; \$320 per bike = \$ 48,000
Total variable costs
=
45,000
Increase in net income
= \$ 3,000
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Break-Even Analysis
Break-even analysis can be
approached in two ways:
1.Equation method
2.Contribution margin
method
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Equation Method
Profits = (Sales – Variable expenses) – Fixed expenses
OR
Sales = Variable expenses + Fixed expenses + Profits
At the break-even point
profits equal zero
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Break-Even Analysis
Here is the information from Racing Bicycle
Company:
Total
Sales (500 bikes)
\$ 250,000
Less: variable expenses 150,000
Contribution margin
\$ 100,000
Less: fixed expenses
80,000
Net operating income
\$ 20,000
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Per Unit
\$
500
300
\$
200
Percent
100%
60%
40%
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Equation Method
We calculate the break-even point as
follows:
Sales = Variable expenses + Fixed expenses + Profits
\$500Q = \$300Q + \$80,000 + \$0
Where:
Q = Number of bikes sold
\$500 = Unit selling price
\$300 = Unit variable expense
\$80,000 = Total fixed expense
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Equation Method
We calculate the break-even point as
follows:
Sales = Variable expenses + Fixed expenses + Profits
\$500Q = \$300Q + \$80,000 + \$0
\$200Q = \$80,000
Q = \$80,000 &divide; \$200 per bike
Q = 400 bikes
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Equation Method
The equation can be modified to calculate the
break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + \$80,000 + \$0
Where:
X = Total sales dollars
0.60 = Variable expenses as a % of sales
\$80,000 = Total fixed expenses
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Equation Method
The equation can be modified to calculate
the break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + \$80,000 + \$0
0.40X = \$80,000
X = \$80,000 &divide; 0.40
X = \$200,000
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Contribution Margin Method
The contribution margin method
has two key equations.
Break-even point
=
in units sold
Break-even point in
total sales dollars =
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Fixed expenses
Unit contribution margin
Fixed expenses
CM ratio
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Contribution Margin Method
Let’s use the contribution margin method to
calculate the break-even point in total
sales dollars at Racing.
Break-even point in
total sales dollars =
Fixed expenses
CM ratio
\$80,000
= \$200,000 break-even sales
40%
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Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per
month is \$1,300. 2,100 cups are sold each
month on average. What is the break-even
sales in units?
a. 872 cups
b. 3,611 cups
c. 1,200 cups
d. 1,150 cups
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EMBA 5403
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. 2,100 cups are sold each month
on average. What is the break-even
sales in
Fixed expenses
Break-even
Unit CM
units?
= \$1,300
a. 872 cups
= \$1.49/cup - \$0.36/cup
b. 3,611 cups
\$1,300
= \$1.13/cup
c. 1,200 cups
= 1,150 cups
d. 1,150 cups
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EMBA 5403
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. 2,100 cups are sold each month
on average. What is the break-even sales in
dollars?
a. \$1,300
b. \$1,715
c. \$1,788
d. \$3,129
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EMBA 5403
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. 2,100 cups are sold each month
on average. What is the break-even sales in
dollars?
Fixed expenses
Break-even
=
a. \$1,300
CM Ratio
sales
\$1,300
b. \$1,715
=
0.758
c. \$1,788
= \$1,715
d. \$3,129
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EMBA 5403
DERIVATION OF EQUATIONS
SALES= VARIABLE COSTS+FIXED COSTS + PROFIT
p*q= vcu *q + FC + &para;
AT BREAKEVEN PROFIT = 0
p*q=vcu *q +FC
q * (p-vcu) = FC
q= FC / (p - vcu) OR q=FC/ cmu
CM= SALES - TOTAL VC
VC= SALES - CM= INCLUDE VARIABLE PRODUCTION AND
SELLING EXPENSES
cmu=CONTRIBUTION MARGIN PER UNIT= p - vcu=CM/q
vcu= VARIABLE COST PER UNIT= VC/ q
q number of units
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PROFIT ANALYSIS
 AT BREAKEVEN PROFIT = 0
 BEFORE BREAKEVEN LOSS; AFTER BREAKEVEN
PROFIT
 CM COVERS FIXED COST UPTO BREAKEVEN POINT
 AFTER BREAKEVEN POINT INCREASE IN CM WILL
INCREASE NET INCOME
 CM = FC + INCOME BEFORE TAX
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Target Profit Analysis
The equation and contribution margin
methods can be used to determine the
sales volume needed to achieve a target
profit.
Suppose Racing Bicycle Company
wants to know how many bikes
must be sold to earn a profit of
\$100,000.
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The CVP Equation Method
Sales = Variable expenses + Fixed expenses + Profits
\$500Q = \$300Q + \$80,000 + \$100,000
\$200Q = \$180,000
Q = 900 bikes
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The Contribution Margin Approach
The contribution margin method can be used
to determine that 900 bikes must be sold to
earn the target profit of \$100,000.
Unit sales to attain
=
the target profit
Fixed expenses + Target profit
Unit contribution margin
\$80,000 + \$100,000
= 900 bikes
\$200/bike
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Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. How many cups of coffee would
have to be sold to attain target profits of
\$2,500 per month?
a. 3,363 cups
b. 2,212 cups
c. 1,150 cups
d. 4,200 cups
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EMBA 5403
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. How many cups of coffee would
have to be sold to attain target profits of
\$2,500 per month?
a. 3,363 cups
b. 2,212 cups
c. 1,150 cups
d. 4,200 cups
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EMBA 5403
Unit breakeven
Unit sales
Fixed expenses + Target profit
to attain =
Unit CM
target profit
\$1,300 + \$2,500
=
\$1.49 - \$0.36
=
\$3,800
\$1.13
= 3,363 cups
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The Margin of Safety
The margin of safety is the excess of
budgeted (or actual) sales over the
break-even volume of sales.
Margin of safety = Total sales - Break-even sales
Let’s look at Racing Bicycle Company and
determine the margin of safety.
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The Margin of Safety
If we assume that Racing Bicycle Company has
actual sales of \$250,000, given that we have
already determined the break-even sales to be
\$200,000, the margin of safety is \$50,000 as
shown
Break-even
sales
400 units
Sales
\$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
\$
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Actual sales
500 units
\$ 250,000
150,000
100,000
80,000
\$
20,000
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The Margin of Safety
The margin of safety can be
expressed as 20% of sales.
(\$50,000 &divide; \$250,000)
Break-even
sales
400 units
Sales
\$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
\$
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Actual sales
500 units
\$ 250,000
150,000
100,000
80,000
\$
20,000
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The Margin of Safety
The margin of safety can be expressed in
terms of the number of units sold. The
margin of safety at Racing is \$50,000,
and each bike sells for \$500.
Margin of
\$50,000
=
= 100 bikes
Safety in units
\$500
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MARGIN OF SAFETY
EXCESS OF SALES (EITHER ACTUAL OR FORECASTED ) OVER
THE BREAKEVEN SALES I.E., THE BUFFER AMOUNT
MoS \$= ACTUAL OR BUDGETED SALES - BREAKEVEN SALES \$
MoS % = MoS \$ / ACTUAL OR BUDGETED SALES
BREAKEVEN SALES IN SINGLE PRODUCT SETTING
SALES \$ = VC\$ + FC\$
WHERE VCR= x% *SALES THEN
1-x% = CMR
SALES \$
= x% *SALES +FC
(1-x)* SALES \$ = FC THAT IS CMR*SALES = FC
SALES \$ AT BREAKEVEN = FC/ CMR
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Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. 2,100 cups are sold each month
on average. What is the margin of safety?
a. 3,250 cups
b. 950 cups
c. 1,150 cups
d. 2,100 cups
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Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. 2,100 cups are sold each month
on average. What is the margin of safety?
a. 3,250 cups
b. 950 cups
c. 1,150 cups
d. 2,100 cups
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Margin of Safety
Margin of safety = Total sales – Break-even sales
= 2,100 cups – 1,150 cups
= 950 cups
or
950 cups
Margin of safety
= 2,100 cups = 45%
percentage
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Cost Structure and Profit
Stability
Cost structure refers to the relative proportion
of fixed and variable costs in an organization.
Managers often have some latitude in
determining their organization’s cost structure.
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Cost Structure and Profit
Stability
fixed cost (or low variable cost) and low fixed
cost (or high variable cost) structures.
An advantage of a high fixed
cost structure is that income
will be higher in good years
compared to companies
A disadvantage of a high fixed
with lower proportion of
cost structure is that income
fixed costs.
will be lower in bad years
compared to companies
with lower proportion of
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fixed
costs.
EMBA 5403
Operating Leverage
 A measure of how sensitive net operating
income is to percentage changes in sales.
Degree of
Contribution margin
=
operating leverage
Net operating income
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Operating Leverage
At Racing, the degree of operating leverage is 5.
Actual sales
500 Bikes
Sales
\$ 250,000
Less: variable expenses
150,000
Contribution margin
100,000
Less: fixed expenses
80,000
Net income
\$ 20,000
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\$100,000
= 5
\$20,000
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Operating Leverage
With an operating leverage of 5, if Racing
increases its sales by 10%, net operating
income would increase by 50%.
Percent increase in sales
Degree of operating leverage
Percent increase in profits
&times;
10%
5
50%
Here’s the verification!
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Operating Leverage
Actual sales
(500)
Sales
\$ 250,000
Less variable expenses
150,000
Contribution margin
100,000
Less fixed expenses
80,000
Net operating income
\$
20,000
Increased
sales (550)
\$ 275,000
165,000
110,000
80,000
\$
30,000
10% increase in sales from
\$250,000 to \$275,000 . . .
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. . . results in a 50% increase in
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income from \$20,000 to \$30,000.
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. 2,100 cups are sold each month
on average. What is the operating leverage?
a. 2.21
b. 0.45
c. 0.34
d. 2.92
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Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is \$1.49 and
the average variable expense per cup is
\$0.36. The average fixed expense per month
is \$1,300. 2,100 cups are sold each month
on average. What is the operating leverage?
a. 2.21
b. 0.45
Operating Contribution margin
c. 0.34
leverage = Net operating income
d. 2.92
\$2,373
= \$1,073 = 2.21
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Con’t
Actual sales
2,100 cups
Sales
\$
3,129
Less: Variable expenses
756
Contribution margin
2,373
Less: Fixed expenses
1,300
Net operating income
\$
1,073
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Quick Check 
At Coffee Klatch the average selling price of a cup
of coffee is \$1.49, the average variable expense per
cup is \$0.36, and the average fixed expense per
month is \$1,300. 2,100 cups are sold each month on
average.
If sales increase by 20%, by how much should net
operating income increase?
a. 30.0%
b. 20.0%
c. 22.1%
d. 44.2%
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Quick Check 
At Coffee Klatch the average selling price of
a cup of coffee is \$1.49, the average variable
expense per cup is \$0.36, and the average
fixed expense per month is \$1,300. 2,100 cups
are sold each month on average.
If sales increase by 20%, by how much
should net operating income increase?
a. 30.0%
Percent increase in sales
20.0%
b. 20.0%
&times; Degree of operating leverage
2.21
c. 22.1%
Percent increase in profit
44.20%
d. 44.2%
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Cost Structure and Operating
Leverage
Operating leverage is greatest in companies that
have a high proportion of fixed costs in relation
to variable costs.
Sales
Variable Expense
CM
Fixed Expenses
Net Income
Operating Leverage Factor
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Company A
\$
500.000
300.000
200.000
150.000
\$
50.000
Company B
\$ 500.000
50.000
450.000
400.000
\$
50.000
200.000
50.000
4
450.000
50.000
9
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Operating Leverage Factor
 A measure of how a percentage
change in sales will affect profits.
Operating leverage
factor
=
Contribution margin
Net income
 The greater the operating
leverage, the greater the
sensitivity of its profit to changes
in volume.
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Operating Leverage Factor
If Company A and B increases
its sales by 10%, which
company will have the
greatest change in net income
and why?
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COST STRUCTURE AND PROFITABILITY






HIGH VARIABLE COSTS LEAD TO LOWER CM AND LESS
VULNERABLE IN CRISIS TIME
HIGH FIXED COSTS CAUSE HIGHER BREAKEVEN POINT;
AFTER THE BREAKEVEN POINT PROFITS INCREASE
FASTER THAN THE HIGH VARIABLE COST COMPANY
DEGREE OF OPERATING LEVERAGE: CONTRIBUTION
MARGIN / NET INCOME
FOR A GIVEN % CHANGE IN SALES, INCOME WILL
INCREASE BY (% INCREASE IN SALES *DEGREE OF
OPERATING LEVERAGE)
DEGREE OF OPERATING LEVERAGE DECREASES AS THE
SALES MOVE AWAY FROM THE BREAKEVEN POINT
IF VARIABLE COSTS ARE HIGH DEGREE OF OPERATING
LEVERAGE LOW; AND VICE VERSA
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Verify Increase in Profit
Actual
sales
2,100 cups
Sales
\$ 3,129
Less: Variable expenses
756
Contribution margin
2,373
Less: Fixed expenses
1,300
Net operating income
\$ 1,073
% change in sales
% change in net operating income
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Increased
sales
2,520 cups
\$
3,755
907
2,848
1,300
\$
1,548
20.0%
44.2%
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Structuring Sales Commissions
Companies generally compensate
salespeople by paying them either a
commission based on sales or a salary plus a
sales commission. Commissions based on
sales dollars can lead to lower profits in a
company.
Let’s look at an example.
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Structuring Sales Commissions
Pipeline Unlimited produces two types of surfboards,
the XR7 and the Turbo. The XR7 sells for \$100 and
generates a contribution margin per unit of \$25. The
Turbo sells for \$150 and earns a contribution margin
per unit of \$18.
The sales force at Pipeline Unlimited is
compensated based on sales commissions.
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Structuring Sales Commissions
If you were on the sales force at Pipeline, you would
push hard to sell the Turbo even though the XR7
earns a higher contribution margin per unit.
To eliminate this type of conflict, commissions can
be based on contribution margin rather than on
selling price alone.
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The Concept of Sales Mix
 Sales mix is the relative proportion in
which a company’s products are sold.
 Different products have different selling
prices, cost structures, and contribution
margins.
Let’s assume Racing Bicycle Company sells
bikes and carts and that the sales mix
between the two products remains the
same.
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Revenue Mix
Revenue mix (or sales mix) is the
relative combination of quantities of
products or services that make up
total revenue
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Pages 73 - 75
Multi-product break-even analysis
Racing Bicycle Co. provides the following information:
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\$265,000
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= 48.2% (rounded)
\$550,000
Multi-product break-even
Break-even
Fixed expenses
=
analysis
sales
CM Ratio
\$170,000
=
48.2%
= \$352,697
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SALES MIX= % OF TOTAL SALES FOR EVERY PRODUCT
THREE PRODUCTS A , B, C
% SALES OF a, b , c where a= sales of product a / total sales etc.
CMa = CM OF PRODUCT A, B OR C
WEIGHTED CMR= a * CMR of product A + b * CMR of product B + c *
CMR of product C
BREAKEVEN IN MULTIPLE PRODUCT S= FC/ WEIGHTED CMR
•TO FIND HOW MANY UNITS MUST BE SOLD AT BREAKEVEN (OR
FOR TARGET INCOME):
1.FIND BREAKEVEN IN MULTIPLE PRODUCTS
2.COMPUTE EACH PRODUCTS SALES AMOUNT BY MULTIPLYING
THE SALES RATIO * BREAKEVEN SALES
3.FIND THE BREAKEVEN SALE SHARE OF EACH PRODUCT;
4.DIVIDE EACH PRODUCTS SHARE OF BREAKEVEN SALES BY
THE UNIT PRICE OF EACH PRODUCT TO GET THE NUMBER OF
UNITS TO BE SOLD OF EACH PRODUCT IN ORDER TO BREAKEVEN
OR FOR TARGET INCOME
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Key Assumptions of CVP
Analysis
 Selling price is constant.
 Costs are linear.
 In multi-product companies, the
sales mix is constant.
 In manufacturing companies,
inventories do not change (units
produced = units sold).
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Multiple Cost Drivers
 In many cases there may be multiple cost drivers
Do-All Software Example
Variable costs:
\$40 per software package sold
\$15 per invoice issued
Operating income
= Revenue – (\$40 x packages sold) – (\$15 x invoices
issued) – Fixed costs
 In cases where there are multiple cost drivers there
are multiple breakeven points
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Examples
 Please do the exercises before the
next session.
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Contribution Margin &amp; Gross Margin
Merchandising Sector
Gross Margin
Format
Contribution Margin
Format
Revenues
Variable costs:
Cost of goods sold
Other variable
Contribution margin
Fixed costs:
Cost of goods sold
\$200
\$120
43
5
163
37
Other fixed
19 24
Operating income \$13
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Revenues
\$200
Cost of goods sold (120+5)
125
Gross margin
75
Operating costs (43+19)
62
Operating income
\$13
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Pages 82 - 83
Example 1: equation approach
•
•
•
•
•
Movie theater: \$48,000 monthly fixed costs
\$8 ticket price.
\$2 variable cost per ticket.
\$6 contribution margin per ticket; 75% cont. margin ratio
Give breakeven units and revenue
BEunits = \$48,000/(\$8 - \$2)
BEunits = 8,000 tickets.
BErevenue = \$64,000
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\$000
(per month)
40
30
Profit
20
Break-even point: 8,000 tickets
10
Profit
area
0
-10
-20
Loss
2,000
4,000
6,000
Loss area
-30
8,000
10,000
Volume of
tickets sold
in one
month
-40
-50
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Fixed expenses = \$48,000
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Example 1 Cont’d
• Suppose practical capacity per month is 12,000
tickets and that the movie theater has operated
at 60% capacity during December. It is now
December 30.
• Has the theater made money in December?
• If they could capture 1,000 customers by
lowering the ticket price to \$7 for New Year’s
Eve, should they do it?
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Example 1 con’t
practical capacity
operating at
contribution
fixed costs
loss
12000 tickets
60%
=60% *12000*6=
43200
48000
-4800
7-2
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1000
5
5000 &gt;
200 net income
yes, they should
4800
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Example 2
Data: The Doral Company manufactures and
sells pens. Present sales output is 5,000,000
per year at a selling price of \$.50 per unit.
Fixed costs are \$900,000 per year. Variable
costs are \$.30 per unit.
 What is the current yearly operating income?
 What is the current breakeven point in sales
dollars?
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Example 2 Cont’d –answer part 1
Contribution margin ratio =
total contribution margin =
Fixed Cost
operating income
Breakeven Sales =
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\$.20/\$.50=
\$1,000,000
\$900,000
\$100,000
40%
900,000/60%=
\$2,250,000
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Example 2 Cont’d – question part 2
Compute the new operating income if . . .
1. A \$.04 per-unit increase in variable
costs.
2. A 20% decrease in fixed costs, a 20%
decrease in selling price, a 10%
decrease in variable costs, and a 40%
increase in units sold.
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Example 2 Cont’d –answer part 2
1. \$0.04 increase in variable costs
new variable cost
0.34
new cont. margin per pen
0.16
total sales
5,000,000 pens
total cont. margin =
\$800,000
Fixed costs
\$900,000
operating income
(\$100,000)
2. A 20% decrease in fixed costs, a 20% decrease in
selling price, a 10% decrease in variable costs, and a
40% increase in units sold.
new selling price
new variable costs
new units sold
total cont. margin =
Fixed costs
operating income
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\$0.40
\$0.27
7,000,000 pens
\$1,890,000
\$900,000
\$990,000
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Example 2 Cont’d-questions part 3
Compute the new breakeven point in units
for
each of the following changes.
 A 10% increase in fixed costs:
 A 10% increase in selling price and a
\$20,000 increase in fixed costs.
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Example 2 Cont’d –answer part 3
new BE units if fixed cost increase by 10%
new fixed costs
contribution margin per pen
New BE units
\$990,000
\$0.20
4,950,000 pens
new BE units if selling price increase by 10%
and fixed cost increase by \$20.000.
\$0.55 per pen
new selling price
\$920,000
new fixed costs
\$0.25 per pen
new contribution margin
3,680,000 pens
New BE units
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Example 3
The Rapid Meal has two restaurants that are open 24
hours per day. Fixed costs for the two restaurants together
total \$450,000 per year. Service varies from a cup of
coffee to full meals. The average sales check for each
customer is \$8.00. The average cost of food and other
variable costs for each customer is \$3.20. The income tax
rate is 30%. Target net income is \$105,000.
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Example 3 Cont’d
Compute the total dollar sales needed
to obtain the target net income.
How many sales checks are needed to
break even?
Compute net income if the number of
sales checks is 150,000
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Compute the total dollar sales needed to obtain the target net income
before tax income= 105000/0.7= \$150,000
approach 1;
sales = vc +fc+before tax profit
sales = average sales check x no of customers
variable cost= vc per cust x no of customers
average check per customer =
8
variable cost per customer =
3.2
approach 2:
contribution margin per customer =
4.8
contribution margin ratio =
0.6
fixed costs =
\$450,000
fixed cost + target income =
\$600,000
Sales to reach target income =
\$1,000,000 (600.000 /0.60)
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How many sales checks are needed to break even?
fixed cost + target income =
contribution margin per customer =
number check (customers) to reach target income
\$600,000
\$4.80
125000
Compute net income if the number of sales checks is 150,000
contribution margin per customer =
number of sales checks (customers)=
total contribution margin
fixed costs =
income before tax
income tax
net income
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\$4.80
150000
\$720,000
\$450,000
\$270,000
81000
\$189,000
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Multiple-Product Example
Assume the following:
Units sold
Sales price per unit
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net income
Regular
Deluxe
Total
Percent
400
\$
500
\$200,000
120,000
\$ 80,000
200
\$750
\$150,000
60,000
\$ 90,000
600
---\$350,000
180,000
\$170,000
130,000
\$ 40,000
=======
------100.0%
51.4
48.6%
1. What is the break even point?
2. How much sales revenue of each product must be generated to earn
a before tax profit \$50,000?
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1. What is the break even point?
fixed costs
weighted cont. margin ratio
BE sales dollars
\$130,000
48.60%
\$267,490
2. How much sales revenue of each product must be generated to earn
a before tax profit \$50,000?
target income
fixed costs
weighted cont. margin ratio
fixed cost + target income
sales revenue targeted- total
sales mix (percent)
regular (200.000/350.000)
deluxe (150.000 / 350.000)
Sales of regular
Sales of deluxe
(sales mix % x sales target)
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\$50,000
\$130,000
48.60%
\$180,000
\$370,370.37
57.14%
42.86%
\$211,640.21
\$158,730.16
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Multiple product - verify
cmr - regular
cmr - deluxe
contribution margin -regular
contribution margin - deluxe
total contribution
Fixed costs
before tax income
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40.00%
60.00%
\$84,656.08
\$95,238.10
\$179,894.18
\$130,000
\$49,894.18
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Example 4
 A financial analyst is studying the feasibility of two
alternative assembly methods, manual and
automated. The automated method has variable
costs of TL 2.10 per unit and annual committed
costs of TL 130.000; in contrast, the manual
method has variable costs of TL 4.20 per unit and
committed costs of TL 60.000. The company sells
its products for TL 23 per unit.
 What is break-even of each method?
 Above what volume level will management prefer
the automated method to the manual method?
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Selling price
Automated
variable
fixed
Example
Manual
variable
fixed
TL23.00
TL2.10 per unit
TL130,000 per year
TL4.20 per unit
TL60,000 per year
Automated BE units:
fixed cost
TL130,000
cont.per unit
TL20.90
BE units
6,220.10
6221 units
Manual BE units:
fixed cost
TL60,000
cont.per unit
TL18.80
BE units
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3,191.49
3.192 units
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Find the indifference point:
2.1q+130000=4.2q+60000
change in cost
TL70,000
change in q
2.1
33333.333 33.334 units
after 33.334 units automated is better
at 35.000 units
at 30.000 units
manual
cont. margin per unit
number of units
Contribution Margin
Fixed Costs
Operating Income
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automated
TL18.80
TL20.90
35000
35000
TL658,000.00 TL731,500.00
manual
cont. margin per unit
number of units
Contribution Margin
TL60,000
TL130,000
Fixed Costs
TL598,000
TL601,500
Operating Income
automated
TL18.80
TL20.90
30000
30000
TL564,000.00 TL627,000.00
TL60,000
TL130,000
TL504,000
TL497,000
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```